Feynman's Rainbow Read online

  Back in my office I licked my wounds. Constantine stopped by and asked a little too cheerily if I was now Schwarz’s latest “disciple.” I made a gesture with my middle finger that they don’t use in either Greece or Italy. But he figured it out.

  What neither of us knew was that within a few years the stack of articles now lying on my desk would be revered worldwide as heralding one of the most promising breakthroughs of the century in theoretical physics.

  X

  IT WAS HARD TO GET a handle on the articles Schwarz handed me, but at least I found myself finally able to focus. I discovered that, despite the dubious reputation of Schwarz and his theory, and his lack of any collaborators on the faculty, he had four or five graduate students working under him, more than any other professor in the department. I spoke with a couple of them when I had questions. They seemed capable. They seemed sane. Didn’t they realize that 99.9 percent of physics “experts” thought they were all crackpots?

  And why did the rest of the faculty allow so many students to go “astray” like this? Someone, I thought, must be a supporter. Could it be Feynman?

  It was a Saturday and the campus was as quiet as the city at daybreak. But this was well past noon, and I was hungry for breakfast. The problem was, though most students lived on campus, on weekends both the Greasy and the Athenaeum were closed. I figured they must eat somewhere, so I went walking outside in search of road kill, or maybe a vending machine. I spotted Feynman a short distance away. I couldn’t imagine why he was there, but I took the opportunity to “bump” into him.

  “Make any discoveries yet?” he said.

  “Right now I’m trying to discover some food. You know where I can eat?”

  “I know where,” he said. “The difficulty lies in the ‘when.’ Weekends, the usual places on campus are closed.”

  We were heading in the direction of the Athenaeum. There seemed to be something going on there. We didn’t talk for a while.

  “Let me ask you something,” I finally said. “Do you think it would be wise to work on a theory that almost everyone else thinks is nonsense?”

  “Only under one condition,” he said.

  “And what is that?”

  “That you don’t think it is nonsense.”

  “I’m not sure I know enough to tell.”

  He chuckled. “Maybe if you knew enough to tell, you wouldn’t work on it, either.”

  “You mean maybe I’m too dumb to know better.”

  “Not necessarily. Maybe you just don’t know enough, or haven’t known it long enough, to be spoiled by what you know. Too much education can cause trouble.”

  It is true that many of the greatest discoveries in physics were made by “kids” who were roughly the age I was. It was the age at which Newton invented calculus, Einstein discovered relativity, and Feynman developed his diagram technique. Plenty of other advances were made by older physicists, but the most revolutionary seemed to be made by the young. It had been understood among us graduate students that, for mathematical and theoretical physics brainpower, our minds were at their peak. But Feynman seemed to be seeing it differently, as if we go downhill not because of mental decline, but due to some kind of brainwashing. Maybe that’s why he avoided learning new things from books or research papers; he was famous for always insisting on deriving new results himself, on understanding them his way. To him, to stay young meant to retain a beginner’s outlook. He had clearly succeeded.

  “Look,” he said. “You’ve found food.”

  There was a big buffet in the Athenaeum courtyard. There seemed to be a wedding reception going on. We stopped and gazed at the crowd in their elegant dresses, suits, and ties.

  “Yeah, but unfortunately we’re not invited.”

  “I see you are an expert in etiquette.”

  “What do you mean?”

  “I mean, if you are not invited, does it mean you aren’t welcome?”

  I shrugged. “I usually assume that.”

  “Then I guess you aren’t that hungry.”

  I thought about it for a moment.

  “Well, we’re not exactly dressed for it.” He had on a dress shirt and slacks. I was clad in shorts and a T-shirt.

  “Of course we aren’t. What scientist goes to work looking like he’s dressed for a wedding? Well, other than Murray.” He laughed.

  “You’ll come with me?” I said.

  He grinned. We headed to the buffet. He looked on as I started loading my plate. At first no one seemed to pay much attention to us, but then a man in a tuxedo came up behind us in line.

  “Bride’s side or groom’s?” the man asked.

  “Neither,” said Feynman. The man looked us up and down. My mind raced, searching for a lie that might minimize my embarrassment. Then Feynman said, “We represent the physics department.”

  The man smiled, took some salad, and walked away, seemingly unbothered by either the answer or our attire.

  XI

  STAYING PLAYFUL, having fun, keeping a youthful outlook. It was clear to me that for Feynman, staying open to all the possibilities of nature, or life, was a key to both his creativity and his happiness.

  I asked him, “Is it foolish to become mature?”

  He thought for a moment. He shrugged.

  I’m not sure. But an important part of the creative process is play. At least for some scientists. It is hard to maintain as you get older. You get less playful. But you shouldn’t, of course.

  I have a large number of entertaining mathematical type of problems, little worlds of this kind that I play in and that I work in from time to time. For example, I first heard about calculus when I was in high school and I saw the formula for the derivative of a function. And the second derivative, and the third. . . . Then I noticed a pattern that worked for the nth derivative, no matter what the integer n was—one, two, three, and so forth.

  But then I asked, what about a “half” derivative? I wanted an operation that when you do it to a function gives you a new function, and if you do it twice you get the ordinary first derivative of the function. Do you know that operation? I invented it when I was in high school. But I didn’t know how to calculate it in those days. I was only in high school, so I could only define it. I couldn’t compute anything. And I didn’t know how to do anything to check it or anything. I just defined it. Only later, when I was in the university, did I start over again. And I had a lot of fun with it. And found out that my original definition that I thought up in high school was right. It would work.

  Then when I was in Los Alamos working on the atomic bomb, I saw some people doing a complicated equation. And I realized that the form they had corresponded to my half derivative. Well, I had invented a numerical operation for solving it, so I did it, and it worked. We checked it by doing it twice, which is just the ordinary derivative. So I did a nifty numerical method for solving their equation. Everything, well, not everything, but lots of stuff turns out to be useful. You just play it out.

  The creative mind has a vast attic. That homework problem you did in college, that intriguing but seemingly pointless paper you spent a week deciphering as a postdoc, that offhand remark of a colleague, all are stored in hope chests somewhere up in a creative person’s brain, often to be picked through and applied by the subconscious at the most unexpected moments. It is a part of the creative process that transcends physics. For instance, Tschaikovsky wrote, “The germ of a future composition comes suddenly and unexpectedly. If the soil is ready . . .” And Mary Shelley: “Invention does not consist in creating out of void, but out of chaos.” And Stephen Spender: “There is nothing we imagine which we do not already know. And our ability to imagine is our ability to remember what we have already once experienced and to apply it to some different situation.”

  Another very interesting and entertaining thing is to ask, if I could change nature in some way, change a physical law, what would happen? First of all, if I would change anything, it would have to be consistent with some other
things. And I have to also work out all of the consequences in this modified law to see what would be happening in the world as a result of this thing. It’s quite an interesting job. It’s a lot of work. And I tried to do that once, I wanted to see how physics would be if it were two-dimensional instead of three-dimensional. Two space dimensions—like Euclid’s plane—plus one time dimension. And there are very, very interesting phenomena like the way atoms behave—their spectral lines, for example. I went through a large number of things that are different in two dimensions versus three dimensions. It’s very interesting. I have it in a notebook. I had a lot of fun doing that.

  By spectral lines, Feynman is referring to the characteristic light that an atom radiates. Adding new spatial dimensions was easy for me to envision. For my dissertation, I, too, had studied how this varies with dimension—all the way from one to infinite dimensions. It was like adding new directions. In one dimension, there is only forward and backward. To get two, you add right and left. For three, up and down. For each additional one, you simply add a new possible independent direction (for some of us, a new possibility for getting lost). It was nice to feel that our imaginations had brought us to envision similar alternative worlds. But I wasn’t ready for the strange place he went next . . .

  And then I had fun doing another one. Suppose there were two times. Two spaces and two times. What kind of world would it be with two times?

  We are accustomed to events having a temporal order. With two time dimensions—if time must be tracked on a plane, rather than a timeline—there would no longer be a strict order to events. It would be a strange world indeed.

  My son and I discussed that on the beach for a long time. He has a lot of good geometrical imagination. He had made a kind of a model by which we could picture this, so we could figure out just what things would look like. So we could picture and ask ourselves questions. What happens and so forth. That’s another game I’d like to play sometime when I have nothing to do.

  We do that all the time, ask, “What if?” and start looking at the consequences. But there are so many things you could change, so that unless you have a good reason, you don’t bother to change these. It takes imagination to find the right one because if you allowed yourself to make simple modifications like that, there are an infinite number of ways that you could modify things, and it would be very hard to select the right one.

  Someone once said, “What if everything was made out of three particles?”

  Feynman is being coy here—the “someone” he is talking about is Murray, and the three particles are his quarks, the particles that are the building blocks for subnuclear particles like the proton.

  Well, then this particle called the K-meson wouldn’t fit into the pattern. No good. What if the charges on the particles were nonintegral, though? Ah! That would account for it! Hey, that’s nifty. Look, that would produce this! That would explain that! That would explain this thing we never understood before! Big excitement! So now we know that things are made out of three particles that do not have normal charges!

  Physicists had noticed long ago that all electric charge seemed to come in multiples of a certain smallest charge. In 1891 Irish physicist George Johnstone Stoney proposed that there existed fundamental, indivisible particles that carried this elementary charge, and coined the word electron. A few years later scientists experimenting with cathode rays observed individual electrons. Since then, no one has ever observed any ion or particle whose charge had a magnitude that was not equal to either 1, 2, 3, or some other integral multiple of the electron’s charge. Thus the concept of a “nonintegral,” or fractional, charge was very controversial when Murray first proposed quarks. Yet, like the mysterious extra dimensions in string theory, it was necessary for the consistency of his theory.

  Cognizant of possible negative reaction, Murray was tentative in his early proposals on quarks. He avoided submitting his initial paper on quarks to the Physical Review, fearful of attacks he expected from its editors and referees, and published it instead in a journal of lesser prestige. Feynman, in the beginning, was one of those skeptical of the quark theory. In the end, his own initial hesitation seemed only to increase his admiration of Murray for having developed it.

  To release yourself from the proposition that all charges have to be an integer, and yet everything you see has an integer charge, that took imagination. It takes imagination to say that charges may not be the way you see them all the time. There is a certain conservatism built in. We have established that things are always integral charges, everywhere. Everywhere! So you figure what everything is made out of is also integral charges. It seemed reasonable, and nobody would think of an alternative because it did not seem necessary, and there was no evidence for it.

  When you’re all finished and you discover something you didn’t expect—something that’s there that you came across—that looks like it’s magic at first! It’s fun! It’s very interesting. I have investigated many little problems. That’s my role.

  Listening to Feynman, I was inspired. Why not release myself from the idea that space-time had four dimensions? So what if string theory required six more? It was a “what-if” I figured deserved more investigation.

  XII

  SPRING WAS NEAR. It’s a nice season in Pasadena—warm weather, but not yet hot, and less rain than winter. A time to enjoy the blue sky, palm trees, and a clear view of the San Gabriel Mountains still blanketed in green. Somehow, somewhere, Ray finally met a girl he liked, or, more to the point, who liked him. The only problem, according to Ray, was that she lived in the state of Washington. Bellevue, to be exact. I saw additional problems. Like the fact that he had decided not to tell her he was a garbage man, only that he worked for the city. And that the only thing they seemed to have in common was that they were both great at math, at least elementary math. But since Ray happened to hate math, I didn’t necessarily see the math connection as a plus. Still, he seemed pretty serious about her, and I was happy for him. He was even thinking of moving to be near her. She did some work for a small software company up there called Microsoft. He thought maybe she could help him get a job. I, of course, selfishly hoped he would stay put.

  Since I often spoke to Ray about the Caltech physics department, and especially of, as he always put it, “that guy Feynman,” Ray decided he wanted to see the place and meet the guy. I agreed, though not without trepidation. Introducing a loquacious cannabis aficionado who hates math but loves talking philosophy to a gruff old professor who likes math, hates talking philosophy, and is fiercely protective of his time is not without risk. But Ray and I were friends, so I agreed to do it.

  Ray often asked me what physicists did, and why they did it. One time I answered him by reciting an Einstein quotation I had read in Zen and the Art of Motorcycle Maintenance: “Man tries to make for himself, in the fashion that suits him best, a simplified and intelligible picture of the world . . . and thus to overcome it. . . . He makes this cosmos and its construction the pivot of his emotional life in order to find in this way the peace and serenity which he cannot find in the whirlpool of personal experience.”

  “That’s just like Einstein,” Ray had said. “His head was way up in the clouds. What I wanna know has to do with planet earth. I wanna know . . . what—do—you—do, and why—do—you—do—it?” He said it as if repeating the question slowly and with emphasis on each word somehow gave it another meaning. If it did, it went over my head. But I thought a visit to campus might provide that picture that was worth a thousand of my ineffectual words.

  On the way over, I tried my detective metaphor.

  “It’s a lot like Sherlock Holmes, or Rockford, depending on your personal style, of course. The first thing is, you have to choose a problem.”

  “Like choosing a crime to work on.”

  “Right. Except detectives are assigned cases. Physicists have to choose for themselves.”

  “Is there the equivalent of the FBI Ten Most Wanted list?”

&
nbsp; “Sure, there’s problems everyone thinks are important. But you’ve got to be careful—a lot of people are working on those. It’s better to find a problem that only you realize is important to solve—that is, if you are right about its being important.”

  “And then you look for clues.”

  “Yeah, but it’s all in your head. You mull over the possibilities, come up with ideas—leads. Then you chase down the leads by fiddling with the mathematics. To figure out if your idea has the consequences you thought, or not. Often that’s not so easy, because you don’t know how to do the math. Am I making sense?”

  “Only in some abstract and totally superficial way.”

  I smiled. “Sounds like progress.”

  After a quick stop in my office we stepped into the hall and walked around the corner. There were already a few graduate students milling around outside the seminar room. Physicists thrive on discussion. They’ll talk physics anywhere, just as anyone else talks about sports or the weather. It gives them a chance to cross-pollinate. That’s how Schwarz made his greatest breakthrough—well, what he considered a breakthrough, anyway. He had been casually chatting with Michael Green in the cafeteria at the European Center for Nuclear Research in Switzerland a couple of years before, when suddenly, together, they realized that string theory was also a theory of gravity. Had they found that, say, quantum chromodynamics could be extended to include gravity, it would have been front-page news around the world and a sure Nobel Prize. But, virtually no one thought string theory was correct. The fact that this incorrect theory might also include a description of gravity did not arouse much excitement among the few who even bothered to listen.

  I had to admire Schwarz—massive rejection didn’t stop him from pushing his theory at every opportunity.

  Today he was giving a seminar on his work with Green. Whenever a faculty member or student has found something worth explaining, and often when he hasn’t, the seminar room is the place to let your colleagues know en masse about your work. In Schwarz’s case, en masse would probably mean only a handful who bothered to show up, but Schwarz always took it with a smile. And he seemed to give more seminars than anyone else in the department.